Generalised common fixed point theorem for weakly compatible mappings via implicit contractive relation in quasi-partial \(S_{b}\)-metric space with some applications. (English) Zbl 07860969
Summary: In the present paper, we prove common fixed point theorems for a pair of weakly compatible mappings under implicit contractive relation in quasi-partial \(S_{b}\)-metric spaces. We also provide an illustrative example to support our results. Furthermore, we will use the results obtained for application to two boundary value problems for the second-order differential equation. Also, we prove a common solution for the nonlinear fractional differential equation.
Keywords:
common fixed point; quasi-partial \(S_{b}\)-metric space; implicit relation; weakly compatible mapping; an integral equation; fractional differential equationReferences:
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